Is it possible after d4 to play c6 and go into the caro-kann or the slav defence?

or is there an other option for white which makes c6 bad?

Well, if you play 1...d5 and 2...c6, White doesn't have the option of going into the Caro-Kann. Perhaps there is some line after 1.d4 c6 2.Nf3 d5 where ...c6 is a bit more passive than you would normally play, but I can't see one right now.

I think it's ok, but don't see why you would prefer it over 1...d5, giving White fewer options.

If you know both the Slav and the Caro but are more comfortable playing the Caro then perhaps this makes sense, since it might tempt White to transpose. I don't see anything better for White than to enter one of those two lines.

I know I'm resurrecting a very dated thread, but I think that 2.e3 moving into a stonewall setup where c6 is not a very helpful move, might be strong against 1..c6

2. e3 isn't fully intending a stonewall just yet, and still can be a transposing move into a c4-d4-e3 formation against the triangle c6-d5-e6 formation. So with that in mind, there's nothing wrong with c6 even against 2. e3.

Most 1.  d4 players aren't going to play 2. e4 against 1. c6 or e6.  Most will probably play either 2. c4 or Nf3.  The only advantage I see to 1. ... c6 is you avoid the Blackmar-Diemer Gambit if that bothers you.  If White plays some other system, say 2. Nc3... you have limited your responses.  At the club level someone might try 2. d5 to screw with your mind but the move itself shouldn't be a problem.

But who said that white has to play c4? He can still play a stonewall.

If you are a beginner, or have a reason for not exploring chess openings, 1...c6 could pretty much be your only move, for "any" white first move... I would not recommend it though, as in my opinion there are better moves in most openings.